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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
20577.2-a1 20577.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.041525978$ $2.801828385$ 3.224348781 \( \frac{1024000}{513} a - \frac{2560000}{513} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -5 a - 3\) , \( 7 a - 1\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(-5a-3\right){x}+7a-1$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.